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The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy. The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi ...
The kinetic energy expression of Thomas–Fermi theory is also used as a component in more sophisticated density approximation to the kinetic energy within modern orbital-free density functional theory. Working independently, Thomas and Fermi used this statistical model in 1927 to approximate the distribution of electrons in an atom.
The Fermi energy defines the energy of the highest energy electron at zero temperature. For metals the Fermi energy is in the order of units of electronvolts above the free electron band minimum energy. [2] In three dimensions, the density of states of a gas of fermions is proportional to the square root of the kinetic energy of the particles.
Numerical solutions of the Thomas–Fermi equation. In mathematics, the Thomas–Fermi equation for the neutral atom is a second order non-linear ordinary differential equation, named after Llewellyn Thomas and Enrico Fermi, [1] [2] which can be derived by applying the Thomas–Fermi model to atoms.
Hence, the internal chemical potential, μ-E 0, is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature T F. This characteristic temperature is on the order of 10 5 K for a metal, hence at room temperature (300 K), the Fermi energy and internal chemical potential are essentially ...
The Thomas–Fermi approximation assumes that the quantum numbers are so large that they may be considered to be a continuum. For large values of n {\displaystyle n} , we can estimate the number of states with energy less than or equal to E {\displaystyle E} from the above equation as:
The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter .
The Fermi velocity can easily be derived from the Fermi energy via the non-relativistic kinetic energy equation. In thin films , however, the film thickness can be smaller than the predicted mean free path, making surface scattering much more noticeable, effectively increasing the resistivity .